1. Field of the Invention
This invention relates to fuzzy logic controllers such as may be used for the control of servo systems or more generally for the control of processes. In particular, the invention relates to a method of tuning the gain of such a fuzzy logic controller.
2. Background Art
Feedback controllers, such as those used for controlling the position of a servo motor, accept a reference input (i.e., a position command indicating the desired position of the motor) and receive a feedback signal (i.e., a signal indicating the actual position of the motor). From these signals, the controller produces a command to the motor or process calculated to bring the feedback signal into closer agreement with the reference input.
For a feedback controller used to control a process, such as fluid level control or temperature control, the reference input indicates the desired output of the process and the controller provides inputs to the process calculated to bring the process output into agreement with the reference input.
In a simple controller, the feedback signal is subtracted from the reference input to produce an error signal and the output of the controller is proportional to the error signal. In more complex controllers, the output is a complex function of the error signal and other signals. The functional relationship between the inputs to the controller and the controller's outputs critically affects the quality of the control as measured in terms of steady state error, overshoot, response time and the controller's ability to handle process nonlinearities such as stiction.
A variety of different functional relationships may be implemented through the use of a Proportional-Integral-Differential ("PID") controller which provides a generalized function which is the sum of: (1) the error signal times a proportional gain factor ("P-gain"), (2) the integral of the error signal times an integral gain factor ("I-gain") and (3) the derivative of the error signal times the derivative gain factor ("D-gain"). This last additive part, D-gain, for practical reasons, may alternatively be a derivative of the feedback signal times a derivative gain factor. Henceforth, these two sources of the derivative signal will be treated as equivalent and used interchangeably.
By adjusting the P-, I- and D-gain factors, a wide variety of transfer functions may be effected which when combined with the physical transfer function of the motor system or process produce the desired system response.
Selecting the proper P-, I- and D-gain factors to produce a desired system response has been the subject of considerable study. If the transfer function of the physical system to be controlled is well known and may be approximated by a linear system, the appropriate P-, I- and D- gain factors may be calculated according to desired tradeoffs by a number of well known methods. More typically, however, the precise transfer characteristics of the physical system are not well known and/or are nonlinear. In these cases, the proper gain factors must be approximated, typically by a human expert applying "rules of thumb".
Fuzzy logic is a well known technique for controlling mathematically ill-understood processes. In fuzzy logic, the rules-of-thumb of experts are captured as fuzzy decision rules that are used to approximate the tradeoffs that would be made by a human expert. A useful overview of fuzzy logic is contained in the article: An Introductory Survey of Fuzzy Control, by Michio Sugeno, in INFORMATION SCIENCES 36, 59-83 (1985) hereby incorporated by reference.
Generally, fuzzy logic first maps one or more analog inputs to several fuzzy states defined by overlapping membership functions. If the input is temperature, the membership functions might be those of "cold", "tepid" or "hot" and serve to characterize any given input as one of these three types to varying degrees.
Fuzzy logic next applies fuzzy rules to the characterized inputs, the fuzzy rules modeling those employed by a human expert, to map the characterized inputs to output states which are described by output membership functions.
The competing membership functions are then combined, in a third "defuzzifying" step, according to one of several methodologies. A common method of combining the output membership functions is to find their center of mass.
The application of fuzzy logic to PID type controllers, although in principle desirable, faces several obstacles. The first obstacle is determining how the fuzzy logic may be incorporated into the architecture of the controller. Fuzzy logic does not have the capacity to develop integrated and differentiated signals, and to use the fuzzy logic simply to sum these signals together, after they are developed by other circuitry, provides very little benefit.
The second obstacle is the development of the rules that the fuzzy logic follows. The fact that fuzzy logic is to be used provides no guidance as to what rules it must follow.
The third obstacle is that of permitting the fine tuning of the fuzzy logic controller to a particular process preferably on a real-time basis. Reprogramming fuzzy logic is, in general, a time consuming and complex process not well suited to fine adjustments.